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Resulting distribution of sample means

Rolling a fair twelve-sided die produces a uniformly distributed set of numbers between 1 and 12 with a mean of 6.5 and a standard deviation of 3.452. Assume that n twelve-sided dice are rolled many times and the mean of the n outcomes is computed each time.

a. Find the mean and standard deviation of the resulting distribution of sample means for n-49.

The mean of the resulting distribution of sample means is?

The standard deviation of the distribution of sample means is?

b. Find the mean and standard deviation of the resulting distribution of sample means for n = 121.

The mean of the resulting distribution of sample means is?

The standard deviation of the distribution of sample means is?

c. Why is the standard deviation in part a different from the standard deviation in part b?

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## Q : Probability of the obtaining

A trick coin has been weighted so that the probability of heads is 0.8 and the probability of tails is 0.2. If you toss the coin 100 times, how many heads would you expect on the average?